Branching programs and binary decision diagrams: theory and applications
Branching programs and binary decision diagrams: theory and applications
Model Checking of Safety Properties
Formal Methods in System Design
Discrete Supervisory Control of Hybrid Systems Based on l-Complete Approximations
Discrete Event Dynamic Systems
Orthogonal Polyhedra: Representation and Computation
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
Controlled Invariance of Discrete Time Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Optimal Semicomputable Approximations to Reachable and Invariant Sets
Theory of Computing Systems
Temporal logic motion planning for dynamic robots
Automatica (Journal of IFAC)
Brief paper: Hierarchical control system design using approximate simulation
Automatica (Journal of IFAC)
Set-Theoretic Methods in Control
Set-Theoretic Methods in Control
Verification and Control of Hybrid Systems: A Symbolic Approach
Verification and Control of Hybrid Systems: A Symbolic Approach
Efficient model checking of safety properties
SPIN'03 Proceedings of the 10th international conference on Model checking software
Model checking LTL over controllable linear systems is decidable
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
PESSOA: a tool for embedded controller synthesis
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
Language-guided controller synthesis for discrete-time linear systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Approximately bisimilar symbolic models for digital control systems
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
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In this paper we present and analyze a novel algorithm to synthesize controllers enforcing linear temporal logic specifications on discrete-time linear systems. The central step within this approach is the computation of the maximal controlled invariant set contained in a possibly non-convex safe set. Although it is known how to compute approximations of maximal controlled invariant sets, its exact computation remains an open problem. We provide an algorithm which computes a controlled invariant set that is guaranteed to be an under-approximation of the maximal controlled invariant set. Moreover, we guarantee that our approximation is at least as good as any invariant set whose distance to the boundary of the safe set is lower bounded. The proposed algorithm is founded on the notion of sets adapted to the dynamics and binary decision diagrams. Contrary to most controller synthesis schemes enforcing temporal logic specifications, we do not compute a discrete abstraction of the continuous dynamics. Instead, we abstract only the part of the continuous dynamics that is relevant for the computation of the maximal controlled invariant set. For this reason we call our approach specification guided. We describe the theoretical foundations and technical underpinnings of a preliminary implementation and report on several experiments including the synthesis of an automatic cruise controller. Our preliminary implementation handles up to five continuous dimensions and specifications containing up to 160 predicates defined as polytopes in about 30 minutes with less than 1 GB memory.